Skip to main content
profile image
Selected Works of Martin Takáč
Article
Inexact Tensor Methods and Their Application to Stochastic Convex Optimization
arXiv
  • Artem Agafonov, Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation & Mohamed bin Zayed University of Artificial Intelligence
  • Dmitry Kamzolov, Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation & Mohamed bin Zayed University of Artificial Intelligence
  • Pavel Dvurechensky, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
  • Alexander Gasnikov, Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation & Institute for Information Transmission Problems, Moscow, Russian Federation & HSE University, Moscow, Russian Federation
  • Martin Takac, Mohamed Bin Zayed University of Artificial Intelligence
Download
Document Type
Article
Abstract

We propose general non-accelerated and accelerated tensor methods under inexact information on the derivatives of the objective, analyze their convergence rate. Further, we provide conditions for the inexactness in each derivative that is sufficient for each algorithm to achieve a desired accuracy. As a corollary, we propose stochastic tensor methods for convex optimization and obtain sufficient mini-batch sizes for each derivative. © 2020, CC BY.

DOI
10.48550/arXiv.2012.15636
Publication Date
12-31-2020
Keywords
  • Stochastic systems,
  • Tensors,
  • Condition,
  • Convergence rates,
  • Convex optimisation,
  • High-order methods,
  • Higher-order methods,
  • Inexact derivative,
  • Objective analysis,
  • Stochastic optimizations,
  • Stochastics,
  • Tensor method,
  • Convex optimization,
  • Optimization and Control (math.OC)
Disciplines
Comments

Preprint: arXiv

Archived with thanks to arXiv

Preprint License: CC by 4.0

Uploaded 13 July 2022

Citation Information
A. Agafonov, D. Kamzolov, P. Dvurechensky, A. Gasnikov, and M. Takac, "Inexact Tensor Methods and Their Application to Stochastic Convex Optimization", 2020, arXiv:2012.15636